The case for the Republic being a Constitution class (and let's remember that no ship was canonically established as a Constitution-class ship until 1987): whenever we saw another starship on the Original Series, it was a Constitution. The name seems to have been used something like Dreadnought originally was in naval affairs, for this one particular model of things. Later the name got generalized, but that often happens to names.Mister_Atoz said:
In regards to the Starship Republic issue, isn't it possible that the ship mentioned in "Court Martial" was an earlier class retired sometime after the events mentioned in the episode, and that a Constitution Class starship named Republic was commissioned later. After all, the aircraft carrier Enterprise which was in service at the time this episode was filmed, is an entirely different ship from the other aircraft carrier named Enterprise in service twenty years before.
Case against: in the first part of ``The Menagerie'', produced essentially simultaneously with ``Court-Martial'' and therefore likely to represent the intentions of the show creators at the time, Pike is explicitly said by Stone to have been injured on an ``inspection tour of a cadet vessel. Old Class J starship.'' As far as I know this is the only mention of alternate classes of starships in the Original Series, but it is there and the intention is obvious: there are older ships which can be used to give cadets experience on real vessels without committing the ships of the line to ferrying them about.
Proposal for my Timo merit badge: the cadets whom Pike saved were part of Class J -- or possibly Jay -- and the starship was an older Constitution-class vessel doing its time as a training vessel. It was the old ``Class J'' starship because it was the old starship given over to Class J. This would be analogous to the way in The Wrath of Khan that the Enterprise was an old training starship, training the new Enterprise Class of cadets.